"My message and my preaching were not with wise and persuasive words, but with a demonstration of the Spirit's power, so that your faith might not rest on men's wisdom, but on God's power." NIV translation
We have probably all heard the expression "Talk is cheap." and it is even true when sharing God's word. Paul's ministry was effective because it was backed up by action and specifically by the action of God through the power of the Spirit. An example of this is found in Acts 19 where people were healed with a handkerchief that Paul had used.
"We do, however, speak a message of wisdom among the mature, but not the wisdom of this age or of the rulers of this age, who are coming to nothing. No, we speak of God's secret wisdom, a wisdom that has been hidden and that God destined for our glory before time began." NIV translation
The wisdom that this passage speaks of is the knowledge of Jesus Christ as the Son of God and Messiah. God knew, from the beginning of creation, that His Son would have to come to save us from sin and death. That did not make much sense to many people in Paul's day and it doesn't make sense to many today. To us that are called, it makes perfect sense.
"None of the rulers of this age understood it, for if they had, they would not have crucified the Lord of glory. However, as it is written: 'No eye has seen, no ear has heard, no mind has conceived what God has prepared for those who love him -'" NIV translation
The leaders of God's people at the time of Jesus' first coming were not ignorant men. They had all of the "book learning" that was available yet they could not see Jesus as the Messiah. Paul quotes from the book of Isaiah and we see that God had even foretold that they would not understand what was to come. Many have used that passage to say that we cannot see or understand what God has prepared for us in eternity but that it not what it is referring to. (We can see what God has prepared for us in Revelation 21)
"but God has revealed it to us by his Spirit. The Spirit searches all things, even the deep things of God. For who among men knows the thoughts of a man except the man's spirit within him? In the same way no one knows the thoughts of God except the Spirit of God." NIV translation
If you want to know the truth about something or someone, then you need to go to the source and it is the same with the things of God. Who better to learn about God than God Himself? We can read and study His word but only God can reveal it to our hearts and that can only happen through the Holy Spirit.